Name each of the following parallelograms:
(i) The diagonals are equal and the adjacent sides are unequal.
(ii) The diagonals are equal and the adjacent sides are equal.
(iii) The diagonals are unequal and the adjacent sides are equal.

Answer

To solve the question, we need to identify the types of parallelograms based on the properties of their diagonals and adjacent sides. Let's break it down step by step.

### Step-by-Step Solution:

1. **Identify the first condition**: The diagonals are equal, and the adjacent sides are unequal.
- **Conclusion**: This type of parallelogram is a **Rectangle**. In a rectangle, the diagonals are equal in length, but the lengths of the adjacent sides can differ.

2. **Identify the second condition**: The diagonals are equal, and the adjacent sides are equal.
- **Conclusion**: This type of parallelogram is a **Square**. A square has all sides equal, and its diagonals are also equal in length.

3. **Identify the third condition**: The diagonals are unequal, and the adjacent sides are equal.
- **Conclusion**: This type of parallelogram is a **Rhombus**. In a rhombus, all sides are equal, but the diagonals are not equal in length.

### Final Answers:
- (i) Rectangle
- (ii) Square
- (iii) Rhombus